Block #358,794

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/14/2014, 8:42:15 AM · Difficulty 10.3846 · 6,432,711 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

49528a0a38d51324b4b2c0a90576bf332fea296fcd8bba080f7095a3da662da4

View on Chainz ↗

Height

#358,794

Difficulty

10.384595

Transactions

Size

1.61 KB

Version

Bits

0a6274d7

Nonce

8,483

Timestamp

1/14/2014, 8:42:15 AM

Confirmations

6,432,711

Merkle Root

871295f0309016f2ffd88165ca476d099e9438c6673650123430c2a2db66210a

Transactions (4)

Coinbasee3e5f7c1fe1636…6d97b6b2d9d818

1 in → 24 out9.2600 XPM879 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 Aac9Hjdg…P4ktypc3 AN6KvTCW…8tVTJUpq AZV4TwxQ…8JnQqSoH

605ce2a3f9c171…18d13cb6021605

1 in → 2 out9.2900 XPM226 B

AGxMeQpn…PtE4vAxN AcBTKmYo…13iUggii

4b5179ce063045…fb213a06b49a7f

1 in → 2 out9.2900 XPM227 B

ARkZjbCM…Y3umdoPx ASGmdnkq…N66cBou7

fd2e823edf0949…e37946e4d25130

1 in → 2 out9.2900 XPM227 B

AVw7nPf6…xQnVWcKB AQDV8G49…VGqpnXjQ

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

8.800 × 10⁹⁵(96-digit number)

88001755395745407315…99527222273094255999

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

8.800 × 10⁹⁵(96-digit number)

88001755395745407315…99527222273094255999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.800 × 10⁹⁵(96-digit number)

88001755395745407315…99527222273094256001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.760 × 10⁹⁶(97-digit number)

17600351079149081463…99054444546188511999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.760 × 10⁹⁶(97-digit number)

17600351079149081463…99054444546188512001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

3.520 × 10⁹⁶(97-digit number)

35200702158298162926…98108889092377023999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.520 × 10⁹⁶(97-digit number)

35200702158298162926…98108889092377024001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

7.040 × 10⁹⁶(97-digit number)

70401404316596325852…96217778184754047999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.040 × 10⁹⁶(97-digit number)

70401404316596325852…96217778184754048001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.408 × 10⁹⁷(98-digit number)

14080280863319265170…92435556369508095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.408 × 10⁹⁷(98-digit number)

14080280863319265170…92435556369508096001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer